Shape key values saved as 0
There's an example of shape keys round-tripping (glTF to Blender to glTF) in the glTF-Blender-IO test suite, which is a collection of .blend files and .gltf files that are used by an automated process to put new versions of the Blender glTF importer/exporter through most of its paces.

The tests/roundtrip/01_cs_morph folder contains a glTF file that is imported and then re-exported, and is expected to preserve the glTF "morph" animation via Blender's shape key animations.

There is also a tests/scenes/01_cs_morph.blend file that is tested via the exporter.  This is a Blender 2.79 project, but the test suite loads it into 2.82 beta (currently) and expects it to export correctly.  You can download the blend file to see how these shape keys look in any recent version of Blender.

It's not clear from the OP screenshots what the problem is there, but start by taking a look at the examples from the test suite to see how it's supposed to work.  If you still have a case where it's broken, please file an issue and include a sample project for testing.